Deviations from the nominal circular symmetry of optical fiber lead to birefringence, resulting in different group velocities for orthogonal polarization modes. Two polarization components of an optical signal thus experience some differential group delay (DGD), which may also change with wavelength. Since optical receivers typically detect the total optical power, irrespective of polarization, DGD manifests itself in pulse spreading, called polarization-mode dispersion (PMD). For a DGD of approximately 10% of the bit period of an optical signal (the exact number depending on modulation format and receiver properties), pulses begin to spread significantly, extending into neighboring bit slots and causing bit errors. Time-varying stresses exerted on the fiber (e.g., mechanical vibrations, temperature variations) randomly change the DGD. Typical rates of change range from milliseconds (due to e.g., acoustic vibrations) to months (for e.g., buried fiber).
PMD-induced signal distortions vary randomly in time, and may lead to error bursts disrupting communication. By the nature of PMD, the amount of signal distortion can be exceedingly large, yet with a very low probability of occurrence. Therefore, systems may occasionally fail, even if high link budget margins are allocated to combat PMD. Given this stochastic behavior of PMD, the typical approach to mitigate the effects of PMD has been to allocate a certain margin to accommodate most instances of PMD-induced signal distortions while leaving the system vulnerable to those random instances in which PMD exceeds this margin. The system's robustness to PMD is then quantified by an outage probability, defined as the probability of PMD-induced error bursts not accommodated for by the allocated margin.
Using traditional models, outage probabilities can be calculated by specifying the deterministic PMD tolerance of a transmitter-receiver pair, and then invoking Maxwellian statistics for the DGD. In this model, Maxwellian statistics apply over time as well as across channels in a wavelength-division multiplexed (WDM) system, and can be used to compute and specify system outage probabilities. Recent studies on the PMD characteristics of a deployed fiber plant suggest a different model with different statistics. (See, e.g., R. Caponi et al., “WDM Design Issues With Highly Correlated PMD Spectra of Buried Optical Cables,” OFC 2002, pp. 453-455.)
As illustrated schematically in FIG. 1, according to the so-called “hinge model,” a typical transmission link 100 consists of several (e.g., 5 to 10) relatively stable, long fiber sections 110 that are well sheltered from the environment over extended periods of time (e.g., months). The sections 110 are referred to as quasi-static waveguide sections or stable fiber sections. On such time scales, the PMD characteristics of these sections are not significantly impacted by temperature variations or mechanical vibrations.
The stable fiber sections 110 are connected by pieces of environmentally unprotected fiber 120 such as dispersion compensating modules at repeater sites, fiber patchcords in switching offices, or lengths of fiber proximate to sources of mechanical vibrations. Such pieces of fiber are referred to as non-static coupling sections or “hinges”. The polarization characteristics of hinges vary rapidly in time.
The hinge model attempts to characterize the PMD statistics of such fiber links. The DGD of the long and stable sections still has a Maxwellian probability density function (PDF) in the wavelength dimension, and essentially does not vary in time. The overall PDF of the link DGD, however, is not Maxwellian. In particular, the DGD at any given wavelength has an upper bound, and each wavelength band (comprising one or more channels) has a different outage probability. Some wavelength bands will comply with a prescribed outage specification while others will not. In other words, no matter what outage probability is specified for a WDM system, a fraction of WDM channels will always violate that outage specification (i.e., a fraction of channels will have a higher-than-specified outage probability). This fraction is quantified by the “non-compliant capacity ratio” (NCR). (See H. Kogelnik et al., “First-Order PMD Outage for the Hinge Model,” IEEE Photonics Technology Letters., Vol. 17, No. 6, June 2005.)
FIG. 2 illustrates the implications of the applicability of the hinge model for the NCR of a typical transmission link with multiple sections. Plot 10 represents the case of the classical model whereas plot 20 represents the hinge model. These plots were derived for a 40 Gb/s fiber link composed of 6 sections (5 hinges), with a mean link DGD of 5 ps, and RZ-OOK modulation. As shown in FIG. 2, the classical model predicts an outage probability of 10−4. This value applies to all WDM channels individually in a statistically independent manner. Under the hinge model, however, for the same link DGD, more than 25% of all WDM channels will be non-compliant, i.e., they will not meet the 10−4 outage specification. On the other hand, approximately 75% of all WDM channels will perform better than specified, and about 45% of all channels will be totally outage-free.
In accordance with the hinge model, the DGD values of each quasi-static section of a link are different for each statistically independent wavelength band. Bands may each contain one or more WDM channels and are considered statistically independent or uncorrelated when their spectral separation exceeds the PMD correlation bandwidth. Depending on how the correlation bandwidth is defined, the PMD correlation bandwidth is approximately between two and six times the bandwidth of the principal state of polarization (BPSP) of a quasi-static link section. WDM channels within a PMD correlation bandwidth are considered to be statistically dependent (or correlated) and will experience the same DGD and outage probability. As such, the NCR pertains to the ensemble of bands making up a WDM system rather than to the individual WDM channels.
Furthermore, as mentioned, while the DGD values of each quasi-static section of a link vary relatively slowly in time (e.g., days to months), they do nonetheless vary. As the DGD values vary, the set of bands that will be non-compliant will also vary. In other words, while the non-compliant capacity (as represented by the NCR) may stay relatively constant, the individual bands constituting that non-compliant capacity will change over time.
In accordance with the hinge model, a multi-section optical communications link will periodically experience severe degradations in performance if all or a significant portion of the WDM channels fall within the non-compliant capacity of the link.